Find the condition for one root of the equation ax2 + bx + c = 0 to be thrice of other root
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5
a x² + b x + c = 0
Root : α , 3 α
so sum: 4 α = -b/a => α = - b/4a
product: 3 α² = c/a
3 (-b/4a)² = c/a
3 b² = 16 c a
This is the condition.
Root : α , 3 α
so sum: 4 α = -b/a => α = - b/4a
product: 3 α² = c/a
3 (-b/4a)² = c/a
3 b² = 16 c a
This is the condition.
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Answered by
1
Let one root be x
then other root will be 3x
x+3x=-b/a ---- 4x=-b/a (i)
x*3x=c/a ---- 3x^2=c/a (ii)
Substituting x form (i) into (ii)
We get,
3b^2=16ac ANS...
then other root will be 3x
x+3x=-b/a ---- 4x=-b/a (i)
x*3x=c/a ---- 3x^2=c/a (ii)
Substituting x form (i) into (ii)
We get,
3b^2=16ac ANS...
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